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Volumn 166, Issue , 2012, Pages 565-600

Projection methods in conic optimization

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EID: 84955102935     PISSN: 08848289     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4614-0769-0_20     Document Type: Chapter
Times cited : (55)

References (75)
  • 1
    • 33847039974 scopus 로고    scopus 로고
    • Solving Hankel matrix approximation problem using semidefinite programming
    • Al-Homidan, S.: Solving Hankel matrix approximation problem using semidefinite programming. Journal of Computational and Applied Mathematics 202(2), 304-314 (2007)
    • (2007) Journal of Computational and Applied Mathematics , vol.202 , Issue.2 , pp. 304-314
    • Al-Homidan, S.1
  • 2
    • 0031141136 scopus 로고    scopus 로고
    • Complementarity and nondegeneracy in semidefinite programming
    • Alizadeh, F., Haeberly, J.-P., Overton, M: Complementarity and nondegeneracy in semidefinite programming. Math. Program. 77(2), 111-128 (1997)
    • (1997) Math. Program , vol.77 , Issue.2 , pp. 111-128
    • Alizadeh, F.1    Haeberly, J.-P.2    Overton, M.3
  • 5
    • 46749136033 scopus 로고    scopus 로고
    • Tame functions are semismooth
    • Bolte, J., Daniilidis, A., Lewis, A.: Tame functions are semismooth. Math. Program. 117(1), 5-19 (2008)
    • (2008) Math. Program , vol.117 , Issue.1 , pp. 5-19
    • Bolte, J.1    Daniilidis, A.2    Lewis, A.3
  • 9
    • 76549100532 scopus 로고    scopus 로고
    • A preconditionned Newton algorithm for the nearest correlation matrix
    • Borsdorf, R., Higham, N.: A preconditionned Newton algorithm for the nearest correlation matrix. IMA J. Numer. Anal. 30(1), 94-107 (2010)
    • (2010) IMA J. Numer. Anal , vol.30 , Issue.1 , pp. 94-107
    • Borsdorf, R.1    Higham, N.2
  • 12
    • 1542307068 scopus 로고    scopus 로고
    • A computational study of a gradient-based log-barrier algorithm for a class of large-scale sdps
    • Burer, S., Monteiro, R., Zhang, Y.: A computational study of a gradient-based log-barrier algorithm for a class of large-scale sdps. Mathematical Programming Series B, 359-379, 2001.
    • (2001) Mathematical Programming Series B , vol.359-379
    • Burer, S.1    Monteiro, R.2    Zhang, Y.3
  • 15
    • 33747195800 scopus 로고    scopus 로고
    • Solving lift-and-project relaxations of binary integer programs
    • Burer, S., Vandenbussche, D.: Solving lift-and-project relaxations of binary integer programs. SIAM Journal on Optimization 16, 726-750 (2006)
    • (2006) SIAM Journal on Optimization , vol.16 , pp. 726-750
    • Burer, S.1    Vandenbussche, D.2
  • 17
    • 33646971357 scopus 로고
    • Convergence of some algorithms for convex minimization
    • Correa, R., Lemaréchal, C.: Convergence of some algorithms for convex minimization. Mathematical Programming 62(2), 261-275 (1993)
    • (1993) Mathematical Programming , vol.62 , Issue.2 , pp. 261-275
    • Correa, R.1    Lemaréchal, C.2
  • 21
    • 84967782959 scopus 로고
    • On the numerical solution of heat conduction problems in two and three space variables
    • Douglas, J., Rachford, H. H.: On the numerical solution of heat conduction problems in two and three space variables. Trans. Amer. Math. Soc. 82, 421-439 (1956)
    • (1956) Trans. Amer. Math. Soc , vol.82 , pp. 421-439
    • Douglas, J.1    Rachford, H.H.2
  • 22
    • 33846706231 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for graph coloring and maximal clique problems
    • Dukanovic, I., Rendl, F.: Semidefinite programming relaxations for graph coloring and maximal clique problems. Mathematical Programming 109, 345-365 (2007)
    • (2007) Mathematical Programming , vol.109 , pp. 345-365
    • Dukanovic, I.1    Rendl, F.2
  • 25
    • 34249975203 scopus 로고
    • Some numerical experiments with variable-storage quasi-Newton algorithms
    • Gilbert, J. C., Lemaréchal, C.: Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming 45, 407-435 (1989)
    • (1989) Mathematical Programming , vol.45 , pp. 407-435
    • Gilbert, J.C.1    Lemaréchal, C.2
  • 26
    • 0002211517 scopus 로고
    • A dual algorithm for the solution of nonlinear variational problems via finite-element approximations
    • Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite-element approximations. Computers and Mathematics with Applications 2 (1976)
    • (1976) Computers and Mathematics with Applications , pp. 2
    • Gabay, D.1    Mercier, B.2
  • 27
    • 84861325244 scopus 로고    scopus 로고
    • Calibrating least squares semidefinite programming with equality and inequality constraints
    • Gao, Y., Sun, D.: Calibrating least squares semidefinite programming with equality and inequality constraints. SIAM J. Matrix Anal. Appl. 31(3), 1432-1457 (2009)
    • (2009) SIAM J. Matrix Anal. Appl , vol.31 , Issue.3 , pp. 1432-1457
    • Gao, Y.1    Sun, D.2
  • 29
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • Goemans, M., Williamson, D.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM 6, 1115-1145 (1995)
    • (1995) Journal of the ACM , vol.6 , pp. 1115-1145
    • Goemans, M.1    Williamson, D.2
  • 31
    • 0000379660 scopus 로고
    • Computing a nearest symmetric positive semidefinite matrix
    • Higham, N.: Computing a nearest symmetric positive semidefinite matrix. Linear Algebra and its Applications 103, 103-118 (1988)
    • (1988) Linear Algebra and its Applications , vol.103 , pp. 103-118
    • Higham, N.1
  • 32
    • 0344153904 scopus 로고    scopus 로고
    • Computing a nearest symmetric correlation matrix-a problem from finance
    • Higham, N.: Computing a nearest symmetric correlation matrix-a problem from finance. IMA Journal of Numerical Analysis 22(3), 329-343 (2002)
    • (2002) IMA Journal of Numerical Analysis , vol.22 , Issue.3 , pp. 329-343
    • Higham, N.1
  • 33
    • 33947537644 scopus 로고    scopus 로고
    • Detecting global optimality and extracting solutions in gloptipoly
    • Henrion, D., Garulli, A., (eds.), LNCIS. Springer
    • Henrion, D., Lasserre, J.-B.: Detecting global optimality and extracting solutions in gloptipoly. In: Henrion, D., Garulli, A., (eds.) Positive polynomials in control, LNCIS. Springer (2005)
    • (2005) Positive polynomials in control
    • Henrion, D.1    Lasserre, J.-B.2
  • 34
    • 77957300831 scopus 로고    scopus 로고
    • Projection methods for conic feasibility problems; application to sumof-squares decompositions
    • Henrion, D., Malick, J.: Projection methods for conic feasibility problems; application to sumof-squares decompositions. Optimization Methods and Software 26(1), 23-46 (2011)
    • (2011) Optimization Methods and Software , vol.26 , Issue.1 , pp. 23-46
    • Henrion, D.1    Malick, J.2
  • 36
    • 0021371266 scopus 로고
    • Generalized hessian matrix and second-order optimality conditions for problems with C1, 1 data
    • Hiriart-Urruty, J.-B., Strodiot, J. J., Nguyen, H. V.: Generalized hessian matrix and second-order optimality conditions for problems with C1, 1 data. Applied Mathematics and Optimization 11, 43-56 (1984)
    • (1984) Applied Mathematics and Optimization , vol.11 , pp. 43-56
    • Hiriart-Urruty, J.-B.1    Strodiot, J.J.2    Nguyen, H.V.3
  • 40
    • 0041844993 scopus 로고    scopus 로고
    • PENNON: A code for convex nonlinear and semidefinite programming
    • Kočvara, M., Stingl, M.: PENNON: a code for convex nonlinear and semidefinite programming. Optimisation Methods and Sofware 18(3), 317-333 (2003)
    • (2003) Optimisation Methods and Sofware , vol.18 , Issue.3 , pp. 317-333
    • Kočvara, M.1    Stingl, M.2
  • 41
    • 33846697416 scopus 로고    scopus 로고
    • On the solution of large-scale sdp problems by the modified barrier method using iterative solvers
    • Kočvara, M., Stingl, M.: On the solution of large-scale sdp problems by the modified barrier method using iterative solvers. Math. Program. 109(2), 413-444 (2007)
    • (2007) Math. Program , vol.109 , Issue.2 , pp. 413-444
    • Kočvara, M.1    Stingl, M.2
  • 42
    • 33747153560 scopus 로고    scopus 로고
    • A sum of squares approximation of nonnegative polynomials
    • Lasserre, J.-B.: A sum of squares approximation of nonnegative polynomials. SIAM J. Optim. 16, 751-765 (2006)
    • (2006) SIAM J. Optim , vol.16 , pp. 751-765
    • Lasserre, J.-B.1
  • 44
    • 67349148256 scopus 로고    scopus 로고
    • Sums of squares, moment matrices and optimization over polynomials
    • M. Putinar and S. Sullivant, editors, IMA Volumes in Mathematics and its Applications. Springer
    • Laurent, M.: Sums of squares, moment matrices and optimization over polynomials. In: M. Putinar and S. Sullivant, editors, Emerging Applications of Algebraic Geometry, IMA Volumes in Mathematics and its Applications. Springer (2009)
    • (2009) Emerging Applications of Algebraic Geometry
    • Laurent, M.1
  • 45
    • 67949083435 scopus 로고    scopus 로고
    • Least-squares approximation of structured covariances
    • Lin, F., Jovanović, M. R.: Least-squares approximation of structured covariances. IEEE Trans. Automat. Control 54(7), 1643-1648 (2009)
    • (2009) IEEE Trans. Automat. Control , vol.54 , Issue.7 , pp. 1643-1648
    • Lin, F.1    Jovanović, M.R.2
  • 46
    • 70349387487 scopus 로고    scopus 로고
    • Local linear convergence for alternating and averaged nonconvex projections
    • Lewis, A., Luke, D., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Foundations of Computational Mathematics 9, 485-513 (2009)
    • (2009) Foundations of Computational Mathematics , vol.9 , pp. 485-513
    • Lewis, A.1    Luke, D.2    Malick, J.3
  • 50
    • 14544268199 scopus 로고    scopus 로고
    • A dual approach to semidefinite least-squares problems
    • Malick, J.: A dual approach to semidefinite least-squares problems. SIAM Journal on Matrix Analysis and Applications 26(1), 272-284 (2004)
    • (2004) SIAM Journal on Matrix Analysis and Applications , vol.26 , Issue.1 , pp. 272-284
    • Malick, J.1
  • 51
  • 53
    • 33746133967 scopus 로고    scopus 로고
    • Clarke generalized Jacobian of the projection onto the cone of positive semidefinite matrices
    • Malick, J., Sendov, H.: Clarke generalized Jacobian of the projection onto the cone of positive semidefinite matrices. Set-Valued Analysis 14(3), 273-293 (2006)
    • (2006) Set-Valued Analysis , vol.14 , Issue.3 , pp. 273-293
    • Malick, J.1    Sendov, H.2
  • 54
    • 0001036636 scopus 로고
    • Smoothing and interpolation in a convex subset of an Hilbert space
    • Micchelli, C. A., Utretas, F. I.: Smoothing and interpolation in a convex subset of an Hilbert space. SIAM J. Sci. Stat. Comput. 9, 728-746 (1988)
    • (1988) SIAM J. Sci. Stat. Comput , vol.9 , pp. 728-746
    • Micchelli, C.A.1    Utretas, F.I.2
  • 55
    • 17444406259 scopus 로고    scopus 로고
    • Smooth minimization of non-smooth functions
    • Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. 103(1), 127-152 (2005)
    • (2005) Math. Program , vol.103 , Issue.1 , pp. 127-152
    • Nesterov, Y.1
  • 59
    • 72449202267 scopus 로고    scopus 로고
    • Model calibration for optical lithography via semidefinite programming
    • Nouralishahi, M., Wu, C., Vandenberghe, L.: Model calibration for optical lithography via semidefinite programming. Optimization and Engineering 9, 19-35 (2008)
    • (2008) Optimization and Engineering , vol.9 , pp. 19-35
    • Nouralishahi, M.1    Wu, C.2    Vandenberghe, L.3
  • 60
    • 33751550994 scopus 로고    scopus 로고
    • A boundary point method to solve semidefinite programs
    • Povh, J., Rendl, F., Wiegele, A.: A boundary point method to solve semidefinite programs. Computing 78, 277-286 (2006)
    • (2006) Computing , vol.78 , pp. 277-286
    • Povh, J.1    Rendl, F.2    Wiegele, A.3
  • 61
    • 5644241870 scopus 로고
    • On an iterative method for linear programming and its economical interpretations
    • Polyak, B. T., Tretjakov, N. V.: On an iterative method for linear programming and its economical interpretations. Èkonom. i Mat. Methody 8, 740-751 (1972)
    • (1972) Èkonom. i Mat. Methody , vol.8 , pp. 740-751
    • Polyak, B.T.1    Tretjakov, N.V.2
  • 62
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • Qi, L. Q., Sun, J.: A nonsmooth version of Newton's method. Mathematical Programming 58(3), 353-367 (1993)
    • (1993) Mathematical Programming , vol.58 , Issue.3 , pp. 353-367
    • Qi, L.Q.1    Sun, J.2
  • 63
    • 34247364678 scopus 로고    scopus 로고
    • Quadratic convergence and numerical experiments of Newton's method for computing the nearest correlation matrix
    • Qi, H., Sun, D.: Quadratic convergence and numerical experiments of Newton's method for computing the nearest correlation matrix. SIAM Journal on Matrix Analysis and Applications 28, 360-385 (2006)
    • (2006) SIAM Journal on Matrix Analysis and Applications , vol.28 , pp. 360-385
    • Qi, H.1    Sun, D.2
  • 65
    • 0016950796 scopus 로고
    • Augmented Lagrangians and applications of the proximal point algorithm in convex programming
    • Rockafellar, R. T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Mathematics of Operations Research 1, 97-116 (1976)
    • (1976) Mathematics of Operations Research , vol.1 , pp. 97-116
    • Rockafellar, R.T.1
  • 69
    • 0033296299 scopus 로고    scopus 로고
    • Using Sedumi 1. 02, a Matlab toolbox for optimization over symmetric cones
    • Sturm, J. F.: Using Sedumi 1. 02, a Matlab toolbox for optimization over symmetric cones. Optmization Methods and Softwares 11-12, 625-653 (1999)
    • (1999) Optmization Methods and Softwares , vol.11-12 , pp. 625-653
    • Sturm, J.F.1
  • 71
    • 77957723364 scopus 로고    scopus 로고
    • A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs
    • Sun, J., Zhang, S.: A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs. European Journal of Operational Research 207(3), 1210-1220 (2003)
    • (2003) European Journal of Operational Research , vol.207 , Issue.3 , pp. 1210-1220
    • Sun, J.1    Zhang, S.2
  • 72
    • 34547439695 scopus 로고    scopus 로고
    • An inexact primal-dual path following algorithm for convex quadratic SDP
    • Toh, K.: An inexact primal-dual path following algorithm for convex quadratic SDP. Math. Program. 112(1), 221-254 (2008)
    • (2008) Math. Program , vol.112 , Issue.1 , pp. 221-254
    • Toh, K.1
  • 73
    • 3142743708 scopus 로고    scopus 로고
    • Solving semidefinite-quadratic-linear programs using SDPT3
    • Tutuncu, R. H., Toh, K. C., Todd, M. J.: Solving semidefinite-quadratic-linear programs using SDPT3. Mathematical Programming B 95, 189-217 (2003)
    • (2003) Mathematical Programming B , vol.95 , pp. 189-217
    • Tutuncu, R.H.1    Toh, K.C.2    Todd, M.J.3
  • 75
    • 77951274410 scopus 로고    scopus 로고
    • A Newton-CG augmented lagrangian method for semidefinite programming
    • Zhao, X., Sun, D., Toh, K.: A Newton-CG augmented lagrangian method for semidefinite programming. SIAM J. Optim 20(4) (2003)
    • (2003) SIAM J. Optim , vol.20 , Issue.4
    • Zhao, X.1    Sun, D.2    Toh, K.3


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